Seriously ill patients with acute renal failure are usually treated with intermittent hemodialysis. This form of treatment has been associated with rapid "unphysiologic" shifts in fluids and solutes which may be detrimental to a patient's well-being and survival. Recently, there has been a growing consensus that a form of continuous renal replacement therapy, which avoids the rapid solute and fluid shifts, may be the treatment of choice for acute renal failure, particularly in critically ill hemodynamically unstable patients. However, so far these two techniques have not been compared in a controlled manner. This study aims to determine the relative efficacy and cost of continuous arteriovenous hemodialysis as compared to acute intermittent hemodialysis in the treatment of acute renal failure in patients hospitalized in the ICU. In addition, it will identify clinical characteristics which identify subgroups of patients most likely to benefit from either of these treatments and also assess the applicability of severity of illness criteria in predicting patient outcome and potential recovery. The study is designed to allocate eligible patients to receive either continuous or intermittent renal replacement therapy in a randomized manner. Nutritional status will be optimized in both groups and several parameters will be followed to assess "severity of illness", renal functional status, and effect on morbidity and mortality. Data will be analyzed to provide information on the efficacy and relative cost of the two techniques and the applicability of derived criteria for predicting patient outcome and assisting in decisions for appropriate use of resources.